Related papers: Constitutive Manifold Neural Networks
Constant-curvature Riemannian manifolds (CCMs) have been shown to be ideal embedding spaces in many application domains, as their non-Euclidean geometry can naturally account for some relevant properties of data, like hierarchy and…
It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
Spiking neural networks (SNNs) can be used in low-power and embedded systems (such as emerging neuromorphic chips) due to their event-based nature. Also, they have the advantage of low computation cost in contrast to conventional artificial…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
Graph Neural Networks (GNNs) have demonstrated impressive capabilities in modeling graph-structured data, while Spiking Neural Networks (SNNs) offer high energy efficiency through sparse, event-driven computation. However, existing spiking…
Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information…
Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
Machine-learning function representations such as neural networks have proven to be excellent constructs for constitutive modeling due to their flexibility to represent highly nonlinear data and their ability to incorporate constitutive…
Learning compressed representations of multivariate time series (MTS) facilitates data analysis in the presence of noise and redundant information, and for a large number of variates and time steps. However, classical dimensionality…
Materials characterization remains a significant, time-consuming undertaking. Generally speaking, spectroscopic techniques are used in conjunction with empirical and ab-initio calculations in order to elucidate structure. These experimental…
Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…
Composite materials like syntactic foams have complex internal microstructures that manifest high-stress concentrations due to material discontinuities occurring from hollow regions and thin walls of hollow particles or microballoons…
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…
Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…
Biological systems leverage top-down feedback for visual processing, yet most artificial vision models succeed in image classification using purely feedforward or recurrent architectures, calling into question the functional significance of…
Deep neural networks (NNs) encounter scalability limitations when confronted with a vast array of neurons, thereby constraining their achievable network depth. To address this challenge, we propose an integration of tensor networks (TN)…
The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…